How do I add thickness to my cardboard cut-out image-as-plane?
I realized that - once again - I'm overthinking this. With more time away, the solution came to me.
In my above question, I identify Step #7 as the issue, but it doesn't have to be. Instead, I realize I should ignore all that goofy geometry. All that matters is I have my ugly extrude with terrible faces.
What I have is that extruded shape set at 0.009 m Z-depth (thin like cardboard). Then I put my 2D plane on it. As long as the material is close to the color of the cardboard (or dominant 2d image color), it will look just fine.
My Current Understanding of Workflow:

Process image to ensure that it has necessary alpha channel. Export a PNG.
Pull image into Illustrator and use the Image Trace option to create a simple outline around the imagery. Export a SVG.
Import Image as Plane; apply additional textures as necessary (if overlaying texture on top of corrugated cardboard texture as I am).
Import SVG as Curves; extrude to needed depth; turn to a mesh.
Place the flat 2D image 'on top of' the 3D mesh that will become the cardboard's faked-depth.
Enter orthographic mode to look at the model head-on. Make final adjustments to ensure the SVG and PNG 'match' locations, as my tests have shown that it won't perfectly match at first. Simply nudge it in ortho and you get your results.


Final note: For whatever reason, when I do this, the 2D image clips into one side of the mesh geometry. Simply adjust the placement (or flip the model over, as I have). This seems to fix it.
Thanks to all of you on my little mini-rollercoaster ride. I will treasure this moment of feeling like I figured something out... because Blender amirite..